Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2640,2,Mod(529,2640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2640.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2640 = 2^{4} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2640.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.0805061336\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.403032 - 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2640.529 |
Dual form | 2640.2.d.i.529.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2640\mathbb{Z}\right)^\times\).
\(n\) | \(661\) | \(881\) | \(991\) | \(1057\) | \(1201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48119 | − | 1.67513i | −0.662410 | − | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.80606i | − | 1.06059i | −0.847812 | − | 0.530296i | \(-0.822081\pi\) | ||
0.847812 | − | 0.530296i | \(-0.177919\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.11871i | 1.41968i | 0.704365 | + | 0.709838i | \(0.251232\pi\) | ||||
−0.704365 | + | 0.709838i | \(0.748768\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67513 | + | 1.48119i | −0.432517 | + | 0.382443i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54420i | 1.10213i | 0.834462 | + | 0.551065i | \(0.185778\pi\) | ||||
−0.834462 | + | 0.551065i | \(0.814222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.57452 | −1.04947 | −0.524733 | − | 0.851267i | \(-0.675835\pi\) | ||||
−0.524733 | + | 0.851267i | \(0.675835\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.80606 | −0.612333 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | + | 4.96239i | −0.122425 | + | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.38787 | 0.443417 | 0.221708 | − | 0.975113i | \(-0.428837\pi\) | ||||
0.221708 | + | 0.975113i | \(0.428837\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.962389 | 0.172850 | 0.0864250 | − | 0.996258i | \(-0.472456\pi\) | ||||
0.0864250 | + | 0.996258i | \(0.472456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.70052 | + | 4.15633i | −0.794533 | + | 0.702547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.61213i | 0.265032i | 0.991181 | + | 0.132516i | \(0.0423056\pi\) | ||||
−0.991181 | + | 0.132516i | \(0.957694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.11871 | 0.819650 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38787 | −0.372923 | −0.186462 | − | 0.982462i | \(-0.559702\pi\) | ||||
−0.186462 | + | 0.982462i | \(0.559702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.80606i | 0.427921i | 0.976842 | + | 0.213960i | \(0.0686363\pi\) | ||||
−0.976842 | + | 0.213960i | \(0.931364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.48119 | + | 1.67513i | 0.220803 | + | 0.249714i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.31265i | 0.629065i | 0.949247 | + | 0.314532i | \(0.101848\pi\) | ||||
−0.949247 | + | 0.314532i | \(0.898152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.873992 | −0.124856 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.54420 | 0.636315 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.57452i | 0.903079i | 0.892251 | + | 0.451540i | \(0.149125\pi\) | ||||
−0.892251 | + | 0.451540i | \(0.850875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.48119 | − | 1.67513i | −0.199724 | − | 0.225875i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.57452i | 0.605909i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.2750 | −1.72826 | −0.864131 | − | 0.503266i | \(-0.832132\pi\) | ||||
−0.864131 | + | 0.503266i | \(0.832132\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.92478 | 1.01466 | 0.507332 | − | 0.861751i | \(-0.330632\pi\) | ||||
0.507332 | + | 0.861751i | \(0.330632\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.80606i | 0.353531i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.57452 | − | 7.58181i | 1.06354 | − | 0.940408i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 10.7005i | − | 1.30728i | −0.756807 | − | 0.653639i | \(-0.773242\pi\) | ||
0.756807 | − | 0.653639i | \(-0.226758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.35026 | 0.872316 | 0.436158 | − | 0.899870i | \(-0.356339\pi\) | ||||
0.436158 | + | 0.899870i | \(0.356339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.41819i | − | 0.751192i | −0.926783 | − | 0.375596i | \(-0.877438\pi\) | ||
0.926783 | − | 0.375596i | \(-0.122562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.96239 | + | 0.612127i | 0.573007 | + | 0.0706823i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.80606i | − | 0.319781i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.35026 | 0.151916 | 0.0759582 | − | 0.997111i | \(-0.475798\pi\) | ||||
0.0759582 | + | 0.997111i | \(0.475798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.806063i | − | 0.0884770i | −0.999021 | − | 0.0442385i | \(-0.985914\pi\) | ||
0.999021 | − | 0.0442385i | \(-0.0140861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.61213 | − | 6.73084i | 0.825651 | − | 0.730062i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.38787i | − | 0.256007i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.96239 | 0.314013 | 0.157006 | − | 0.987598i | \(-0.449816\pi\) | ||||
0.157006 | + | 0.987598i | \(0.449816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.3634 | 1.50570 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 0.962389i | − | 0.0997950i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.77575 | + | 7.66291i | 0.695177 | + | 0.786198i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.92478i | − | 1.00771i | −0.863789 | − | 0.503854i | \(-0.831915\pi\) | ||
0.863789 | − | 0.503854i | \(-0.168085\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.6121 | −1.35446 | −0.677229 | − | 0.735773i | \(-0.736819\pi\) | ||||
−0.677229 | + | 0.735773i | \(0.736819\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3127i | 1.60733i | 0.595080 | + | 0.803667i | \(0.297120\pi\) | ||||
−0.595080 | + | 0.803667i | \(0.702880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.15633 | + | 4.70052i | 0.405616 | + | 0.458724i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.43136i | 0.911764i | 0.890040 | + | 0.455882i | \(0.150676\pi\) | ||||
−0.890040 | + | 0.455882i | \(0.849324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.4010 | 1.47515 | 0.737576 | − | 0.675264i | \(-0.235970\pi\) | ||||
0.737576 | + | 0.675264i | \(0.235970\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.61213 | 0.153016 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.7381i | 1.29238i | 0.763179 | + | 0.646188i | \(0.223638\pi\) | ||||
−0.763179 | + | 0.646188i | \(0.776362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.70052 | − | 5.92478i | 0.624827 | − | 0.552488i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.11871i | − | 0.473225i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.7513 | 1.16891 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.38787i | 0.215307i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.21933 | − | 6.32487i | 0.824602 | − | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.4182i | − | 1.10194i | −0.834526 | − | 0.550968i | \(-0.814259\pi\) | ||
0.834526 | − | 0.550968i | \(-0.185741\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.80606 | 0.247060 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.92478 | −0.517650 | −0.258825 | − | 0.965924i | \(-0.583335\pi\) | ||||
−0.258825 | + | 0.965924i | \(0.583335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8364i | 1.11306i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.67513 | − | 1.48119i | 0.144172 | − | 0.127481i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.79877i | 0.837165i | 0.908179 | + | 0.418583i | \(0.137473\pi\) | ||||
−0.908179 | + | 0.418583i | \(0.862527\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.12601 | −0.180326 | −0.0901628 | − | 0.995927i | \(-0.528739\pi\) | ||||
−0.0901628 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31265 | 0.363191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.11871i | 0.428048i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.53690 | − | 4.00000i | −0.293724 | − | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.873992i | 0.0720856i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.31265 | −0.680999 | −0.340499 | − | 0.940245i | \(-0.610596\pi\) | ||||
−0.340499 | + | 0.940245i | \(0.610596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.2750 | 1.24307 | 0.621533 | − | 0.783388i | \(-0.286510\pi\) | ||||
0.621533 | + | 0.783388i | \(0.286510\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.54420i | − | 0.367377i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.42548 | − | 1.61213i | −0.114498 | − | 0.129489i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.01317i | 0.559712i | 0.960042 | + | 0.279856i | \(0.0902868\pi\) | ||||
−0.960042 | + | 0.279856i | \(0.909713\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.57452 | 0.521393 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.2243 | 0.884595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.76116i | 0.529575i | 0.964307 | + | 0.264787i | \(0.0853018\pi\) | ||||
−0.964307 | + | 0.264787i | \(0.914698\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.67513 | + | 1.48119i | −0.130409 | + | 0.115311i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.8192i | 0.914600i | 0.889312 | + | 0.457300i | \(0.151183\pi\) | ||||
−0.889312 | + | 0.457300i | \(0.848817\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2012 | −1.01548 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.57452 | 0.349822 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.99271i | − | 0.531646i | −0.964022 | − | 0.265823i | \(-0.914356\pi\) | ||
0.964022 | − | 0.265823i | \(-0.0856436\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.9248 | + | 1.71767i | 1.05261 | + | 0.129843i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2750i | 0.997813i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.70052 | −0.201847 | −0.100923 | − | 0.994894i | \(-0.532180\pi\) | ||||
−0.100923 | + | 0.994894i | \(0.532180\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.1998 | −1.57577 | −0.787885 | − | 0.615822i | \(-0.788824\pi\) | ||||
−0.787885 | + | 0.615822i | \(0.788824\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.92478i | − | 0.585816i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.70052 | − | 2.38787i | 0.198546 | − | 0.175560i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.54420i | 0.332305i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.80606 | 0.204111 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.1490 | −0.951430 | −0.475715 | − | 0.879599i | \(-0.657811\pi\) | ||||
−0.475715 | + | 0.879599i | \(0.657811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 5.89446i | − | 0.424293i | −0.977238 | − | 0.212146i | \(-0.931955\pi\) | ||
0.977238 | − | 0.212146i | \(-0.0680453\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.58181 | − | 8.57452i | −0.542945 | − | 0.614034i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3938i | 1.45299i | 0.687169 | + | 0.726497i | \(0.258853\pi\) | ||||
−0.687169 | + | 0.726497i | \(0.741147\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.4010 | 1.23353 | 0.616764 | − | 0.787148i | \(-0.288443\pi\) | ||||
0.616764 | + | 0.787148i | \(0.288443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.7005 | −0.754757 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.70052i | − | 0.470285i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.53690 | + | 4.00000i | 0.247028 | + | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 4.00000i | − | 0.278019i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.57452 | −0.316426 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.1260 | −1.24785 | −0.623923 | − | 0.781486i | \(-0.714462\pi\) | ||||
−0.623923 | + | 0.781486i | \(0.714462\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 7.35026i | − | 0.503632i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.70052 | − | 4.15633i | 0.320573 | − | 0.283459i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.70052i | − | 0.183323i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.41819 | −0.433701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.2605 | −1.56467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.6385i | 1.58295i | 0.611202 | + | 0.791475i | \(0.290686\pi\) | ||||
−0.611202 | + | 0.791475i | \(0.709314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.612127 | − | 4.96239i | 0.0408085 | − | 0.330826i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.26916i | 0.0842371i | 0.999113 | + | 0.0421185i | \(0.0134107\pi\) | ||||
−0.999113 | + | 0.0421185i | \(0.986589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.1768 | −1.06899 | −0.534496 | − | 0.845171i | \(-0.679499\pi\) | ||||
−0.534496 | + | 0.845171i | \(0.679499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.80606 | −0.184625 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.4690i | 1.20994i | 0.796247 | + | 0.604971i | \(0.206815\pi\) | ||||
−0.796247 | + | 0.604971i | \(0.793185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.22425 | − | 6.38787i | 0.471258 | − | 0.416699i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.35026i | − | 0.0877089i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.3258 | 1.25008 | 0.625042 | − | 0.780591i | \(-0.285082\pi\) | ||||
0.625042 | + | 0.780591i | \(0.285082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.5501 | 1.83907 | 0.919536 | − | 0.393006i | \(-0.128565\pi\) | ||||
0.919536 | + | 0.393006i | \(0.128565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.29455 | + | 1.46405i | 0.0827059 | + | 0.0935348i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 23.4156i | − | 1.48990i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.806063 | −0.0510822 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.1998 | −1.46436 | −0.732180 | − | 0.681112i | \(-0.761497\pi\) | ||||
−0.732180 | + | 0.681112i | \(0.761497\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000i | 0.251478i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.73084 | − | 7.61213i | −0.421502 | − | 0.476690i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 10.8872i | − | 0.679123i | −0.940584 | − | 0.339561i | \(-0.889721\pi\) | ||
0.940584 | − | 0.339561i | \(-0.110279\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.52373 | 0.281091 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.38787 | −0.147806 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.11871i | 0.562284i | 0.959666 | + | 0.281142i | \(0.0907132\pi\) | ||||
−0.959666 | + | 0.281142i | \(0.909287\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0132 | − | 9.73813i | 0.676534 | − | 0.598209i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2.96239i | − | 0.181295i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2995 | 0.688941 | 0.344471 | − | 0.938797i | \(-0.388058\pi\) | ||||
0.344471 | + | 0.938797i | \(0.388058\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1998 | −1.53078 | −0.765390 | − | 0.643567i | \(-0.777454\pi\) | ||||
−0.765390 | + | 0.643567i | \(0.777454\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 14.3634i | − | 0.869315i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.612127 | + | 4.96239i | −0.0369126 | + | 0.299243i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.41819i | − | 0.145295i | −0.997358 | − | 0.0726475i | \(-0.976855\pi\) | ||
0.997358 | − | 0.0726475i | \(-0.0231448\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.962389 | −0.0576167 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.4894 | 1.81885 | 0.909424 | − | 0.415870i | \(-0.136523\pi\) | ||||
0.909424 | + | 0.415870i | \(0.136523\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.35756i | 0.496805i | 0.968657 | + | 0.248403i | \(0.0799056\pi\) | ||||
−0.968657 | + | 0.248403i | \(0.920094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.66291 | − | 6.77575i | 0.453912 | − | 0.401361i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.70052i | 0.395519i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.64974 | −0.214690 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.92478 | −0.581801 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.0943i | 1.34918i | 0.738192 | + | 0.674591i | \(0.235680\pi\) | ||||
−0.738192 | + | 0.674591i | \(0.764320\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.6629 | + | 22.2374i | 1.14482 | + | 1.29471i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.4749 | −1.18409 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.87399 | 0.453849 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.6121i | 0.781996i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.7381 | − | 13.2750i | −0.672124 | − | 0.760127i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.65562i | − | 0.151564i | −0.997124 | − | 0.0757821i | \(-0.975855\pi\) | ||
0.997124 | − | 0.0757821i | \(-0.0241453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3127 | 0.927994 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.9756 | 0.905891 | 0.452946 | − | 0.891538i | \(-0.350373\pi\) | ||||
0.452946 | + | 0.891538i | \(0.350373\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0606343i | 0.00342726i | 0.999999 | + | 0.00171363i | \(0.000545465\pi\) | ||||
−0.999999 | + | 0.00171363i | \(0.999455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.70052 | − | 4.15633i | 0.264844 | − | 0.234182i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.81336i | 0.214180i | 0.994249 | + | 0.107090i | \(0.0341532\pi\) | ||||
−0.994249 | + | 0.107090i | \(0.965847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.38787 | 0.133695 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.43136 | 0.526407 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.7875i | − | 1.15665i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.4010 | − | 3.13330i | −1.40900 | − | 0.173804i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 15.4010i | − | 0.851680i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.1016 | 0.667181 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.2882 | −1.33500 | −0.667500 | − | 0.744609i | \(-0.732636\pi\) | ||||
−0.667500 | + | 0.744609i | \(0.732636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.61213i | − | 0.0883440i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.9248 | + | 15.8496i | −0.979335 | + | 0.865954i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 22.5804i | − | 1.23003i | −0.788514 | − | 0.615016i | \(-0.789149\pi\) | ||
0.788514 | − | 0.615016i | \(-0.210851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.7381 | 0.746153 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.962389 | 0.0521163 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.1900i | − | 0.928171i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.92478 | − | 6.70052i | −0.318979 | − | 0.360744i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.1925i | − | 1.08399i | −0.840381 | − | 0.541996i | \(-0.817669\pi\) | ||
0.840381 | − | 0.541996i | \(-0.182331\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.2506 | 1.45869 | 0.729346 | − | 0.684145i | \(-0.239825\pi\) | ||||
0.729346 | + | 0.684145i | \(0.239825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11871 | −0.273217 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.02302i | − | 0.267349i | −0.991025 | − | 0.133674i | \(-0.957322\pi\) | ||
0.991025 | − | 0.133674i | \(-0.0426776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.8872 | − | 12.3127i | −0.577831 | − | 0.653488i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 12.7513i | − | 0.674871i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1768 | −0.959334 | −0.479667 | − | 0.877450i | \(-0.659243\pi\) | ||||
−0.479667 | + | 0.877450i | \(0.659243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.92619 | 0.101379 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.7513 | + | 9.50659i | −0.562749 | + | 0.497598i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.56467i | 0.447072i | 0.974696 | + | 0.223536i | \(0.0717600\pi\) | ||||
−0.974696 | + | 0.223536i | \(0.928240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.38787 | 0.124308 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.4485 | 0.957799 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 7.81924i | − | 0.404865i | −0.979296 | − | 0.202432i | \(-0.935115\pi\) | ||
0.979296 | − | 0.202432i | \(-0.0648846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.32487 | − | 9.21933i | −0.326615 | − | 0.476084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2228i | 0.629508i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.14903 | 0.0590218 | 0.0295109 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295109 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.4182 | −0.636203 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.0870i | 1.74176i | 0.491493 | + | 0.870882i | \(0.336451\pi\) | ||||
−0.491493 | + | 0.870882i | \(0.663549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.70052 | + | 4.15633i | −0.239561 | + | 0.211826i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.80606i | − | 0.142640i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.7743 | −1.20541 | −0.602703 | − | 0.797965i | \(-0.705910\pi\) | ||||
−0.602703 | + | 0.797965i | \(0.705910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.1768 | −0.919240 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.92478i | 0.298865i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.00000 | − | 2.26187i | −0.100631 | − | 0.113807i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 4.15045i | − | 0.208305i | −0.994561 | − | 0.104152i | \(-0.966787\pi\) | ||
0.994561 | − | 0.104152i | \(-0.0332130\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.8364 | 0.642623 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −33.9149 | −1.69363 | −0.846815 | − | 0.531887i | \(-0.821483\pi\) | ||||
−0.846815 | + | 0.531887i | \(0.821483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.92619i | 0.245391i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.48119 | − | 1.67513i | −0.0736011 | − | 0.0832379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.61213i | 0.0799102i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.55008 | −0.422774 | −0.211387 | − | 0.977402i | \(-0.567798\pi\) | ||||
−0.211387 | + | 0.977402i | \(0.567798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.79877 | 0.483338 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 37.2506i | 1.83298i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.35026 | + | 1.19394i | −0.0662817 | + | 0.0586080i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.12601i | 0.104111i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2995 | 0.649722 | 0.324861 | − | 0.945762i | \(-0.394682\pi\) | ||||
0.324861 | + | 0.945762i | \(0.394682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3014 | 1.62301 | 0.811505 | − | 0.584345i | \(-0.198649\pi\) | ||||
0.811505 | + | 0.584345i | \(0.198649\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 4.31265i | − | 0.209688i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.5501 | − | 2.78163i | −1.09384 | − | 0.134929i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 22.2374i | − | 1.07614i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.11871 | 0.247134 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.07522 | −0.0999600 | −0.0499800 | − | 0.998750i | \(-0.515916\pi\) | ||||
−0.0499800 | + | 0.998750i | \(0.515916\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.4010i | 1.79738i | 0.438585 | + | 0.898690i | \(0.355480\pi\) | ||||
−0.438585 | + | 0.898690i | \(0.644520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.00000 | + | 3.53690i | −0.191785 | + | 0.169582i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 18.2981i | − | 0.875315i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.02444 | −0.287531 | −0.143765 | − | 0.989612i | \(-0.545921\pi\) | ||||
−0.143765 | + | 0.989612i | \(0.545921\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.873992 | 0.0416187 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 10.1359i | − | 0.481569i | −0.970579 | − | 0.240785i | \(-0.922595\pi\) | ||
0.970579 | − | 0.240785i | \(-0.0774047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.38787 | − | 4.96239i | −0.208005 | − | 0.235240i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.31265i | 0.393175i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.4861 | 0.542063 | 0.271032 | − | 0.962570i | \(-0.412635\pi\) | ||||
0.271032 | + | 0.962570i | \(0.412635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.38787 | −0.112441 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 15.2750i | − | 0.717684i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −21.2750 | − | 24.0606i | −0.997389 | − | 1.12798i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.0435i | − | 0.703705i | −0.936055 | − | 0.351852i | \(-0.885552\pi\) | ||
0.936055 | − | 0.351852i | \(-0.114448\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.54420 | −0.212105 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.2374 | −1.22200 | −0.610999 | − | 0.791631i | \(-0.709232\pi\) | ||||
−0.610999 | + | 0.791631i | \(0.709232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.46168i | − | 0.253826i | −0.991914 | − | 0.126913i | \(-0.959493\pi\) | ||
0.991914 | − | 0.126913i | \(-0.0405069\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.61213 | + | 1.42548i | −0.0747606 | + | 0.0661053i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.70052i | 0.124965i | 0.998046 | + | 0.0624827i | \(0.0199018\pi\) | ||||
−0.998046 | + | 0.0624827i | \(0.980098\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0263 | −1.38649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.01317 | 0.323150 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.80606i | 0.129023i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.80018 | − | 22.7005i | 0.128481 | − | 1.04157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.57452i | − | 0.301026i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.7757 | 0.766503 | 0.383252 | − | 0.923644i | \(-0.374804\pi\) | ||||
0.383252 | + | 0.923644i | \(0.374804\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.25202 | −0.376260 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 11.2243i | − | 0.510721i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.6253 | + | 14.7005i | −0.754916 | + | 0.667516i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.3996i | 1.55880i | 0.626529 | + | 0.779398i | \(0.284475\pi\) | ||||
−0.626529 | + | 0.779398i | \(0.715525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.76116 | 0.305750 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.9525 | −0.674799 | −0.337399 | − | 0.941362i | \(-0.609547\pi\) | ||||
−0.337399 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.8510i | 0.488703i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.48119 | + | 1.67513i | 0.0665747 | + | 0.0752915i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 20.6253i | − | 0.925171i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.85097 | −0.127627 | −0.0638135 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638135 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.8192 | 0.528045 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.48024i | 0.0660006i | 0.999455 | + | 0.0330003i | \(0.0105062\pi\) | ||||
−0.999455 | + | 0.0330003i | \(0.989494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.1622 | + | 22.8021i | 0.897206 | + | 1.01468i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.2012i | 0.586287i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.2995 | 1.03273 | 0.516366 | − | 0.856368i | \(-0.327285\pi\) | ||||
0.516366 | + | 0.856368i | \(0.327285\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.0098 | −0.796709 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.57452i | − | 0.201970i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.3258 | − | 24.1622i | 1.20412 | − | 1.06471i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.31265i | 0.189670i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.99271 | −0.306946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.81194 | −0.298437 | −0.149218 | − | 0.988804i | \(-0.547676\pi\) | ||||
−0.149218 | + | 0.988804i | \(0.547676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0567i | − | 0.702109i | −0.936355 | − | 0.351054i | \(-0.885823\pi\) | ||
0.936355 | − | 0.351054i | \(-0.114177\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.71767 | − | 13.9248i | 0.0749651 | − | 0.607727i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.37328i | 0.190503i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.2750 | 0.576088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.2228i | − | 0.529430i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7988 | − | 13.9697i | 0.683040 | − | 0.603962i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.70052i | 0.116536i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.873992 | −0.0376455 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.62530 | 0.284844 | 0.142422 | − | 0.989806i | \(-0.454511\pi\) | ||||
0.142422 | + | 0.989806i | \(0.454511\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1998i | 0.909771i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.8119 | − | 25.7988i | −0.977156 | − | 1.10510i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.75860i | 0.246220i | 0.992393 | + | 0.123110i | \(0.0392868\pi\) | ||||
−0.992393 | + | 0.123110i | \(0.960713\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.92478 | −0.338221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.9234 | −0.465351 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.78892i | − | 0.161121i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.38787 | − | 2.70052i | −0.101360 | − | 0.114631i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.8700i | 0.841920i | 0.907079 | + | 0.420960i | \(0.138307\pi\) | ||||
−0.907079 | + | 0.420960i | \(0.861693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.3634 | −0.607509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.54420 | 0.191856 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.83383i | 0.245866i | 0.992415 | + | 0.122933i | \(0.0392301\pi\) | ||||
−0.992415 | + | 0.122933i | \(0.960770\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.0132 | − | 20.3488i | 0.968171 | − | 0.856082i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.80606i | − | 0.117844i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.7123 | −1.95828 | −0.979140 | − | 0.203185i | \(-0.934871\pi\) | ||||
−0.979140 | + | 0.203185i | \(0.934871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.4241 | 1.02212 | 0.511058 | − | 0.859546i | \(-0.329254\pi\) | ||||
0.511058 | + | 0.859546i | \(0.329254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.1490i | 0.549309i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.8496 | − | 2.44851i | −0.827784 | − | 0.102110i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.5647i | 0.689596i | 0.938677 | + | 0.344798i | \(0.112053\pi\) | ||||
−0.938677 | + | 0.344798i | \(0.887947\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.89446 | −0.244965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.26187 | −0.0938380 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.57452i | 0.272289i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.57452 | + | 7.58181i | −0.354513 | + | 0.313469i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 27.3258i | − | 1.12786i | −0.825823 | − | 0.563929i | \(-0.809289\pi\) | ||
0.825823 | − | 0.563929i | \(-0.190711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.40246 | −0.181400 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.3938 | 0.838887 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.6048i | 0.517618i | 0.965928 | + | 0.258809i | \(0.0833301\pi\) | ||||
−0.965928 | + | 0.258809i | \(0.916670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.8872 | − | 21.3601i | −0.774298 | − | 0.875679i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 17.4010i | − | 0.712177i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5990 | 0.433061 | 0.216531 | − | 0.976276i | \(-0.430526\pi\) | ||||
0.216531 | + | 0.976276i | \(0.430526\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.4749 | −0.916768 | −0.458384 | − | 0.888754i | \(-0.651572\pi\) | ||||
−0.458384 | + | 0.888754i | \(0.651572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.7005i | 0.435759i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.48119 | − | 1.67513i | −0.0602191 | − | 0.0681038i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 33.5183i | − | 1.36047i | −0.732995 | − | 0.680234i | \(-0.761878\pi\) | ||
0.732995 | − | 0.680234i | \(-0.238122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.70052 | −0.271519 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.0752 | −0.893068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 11.5672i | − | 0.467196i | −0.972333 | − | 0.233598i | \(-0.924950\pi\) | ||
0.972333 | − | 0.233598i | \(-0.0750499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.00000 | − | 3.53690i | 0.161296 | − | 0.142622i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 33.3357i | − | 1.34204i | −0.741438 | − | 0.671022i | \(-0.765856\pi\) | ||
0.741438 | − | 0.671022i | \(-0.234144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.43866 | 0.178405 | 0.0892024 | − | 0.996014i | \(-0.471568\pi\) | ||||
0.0892024 | + | 0.996014i | \(0.471568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.00000 | −0.160514 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8.31265i | − | 0.333039i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | − | 6.07522i | −0.970024 | − | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.57452i | 0.182689i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.32582 | −0.292100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.8496 | 1.58639 | 0.793193 | − | 0.608971i | \(-0.208417\pi\) | ||||
0.793193 | + | 0.608971i | \(0.208417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.1260i | 0.720444i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.8021 | + | 18.3938i | −0.825506 | + | 0.729934i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.47371i | − | 0.177255i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.35026 | −0.290772 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.88858 | −0.153590 | −0.0767948 | − | 0.997047i | \(-0.524469\pi\) | ||||
−0.0767948 | + | 0.997047i | \(0.524469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.9380i | 1.61444i | 0.590254 | + | 0.807218i | \(0.299028\pi\) | ||||
−0.590254 | + | 0.807218i | \(0.700972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.15633 | − | 4.70052i | −0.163655 | − | 0.185083i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1.76257i | − | 0.0692939i | −0.999400 | − | 0.0346469i | \(-0.988969\pi\) | ||
0.999400 | − | 0.0346469i | \(-0.0110307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2750 | −0.521091 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.70052 | −0.105842 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.03761i | 0.275403i | 0.990474 | + | 0.137702i | \(0.0439715\pi\) | ||||
−0.990474 | + | 0.137702i | \(0.956029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.77575 | + | 9.92478i | 0.342897 | + | 0.387793i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.41819i | 0.250397i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.6253 | −0.491812 | −0.245906 | − | 0.969294i | \(-0.579085\pi\) | ||||
−0.245906 | + | 0.969294i | \(0.579085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.2243 | 0.514364 | 0.257182 | − | 0.966363i | \(-0.417206\pi\) | ||||
0.257182 | + | 0.966363i | \(0.417206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.2605i | 0.903361i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.5026 | − | 19.0132i | 0.833836 | − | 0.737299i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.55149i | 0.369835i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.6385 | 0.913916 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.92478 | 0.305933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 18.2677i | − | 0.704170i | −0.935968 | − | 0.352085i | \(-0.885473\pi\) | ||
0.935968 | − | 0.352085i | \(-0.114527\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.96239 | − | 0.612127i | −0.191002 | − | 0.0235608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 33.0191i | − | 1.26903i | −0.772912 | − | 0.634513i | \(-0.781201\pi\) | ||
0.772912 | − | 0.634513i | \(-0.218799\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.8496 | −1.06877 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.26916 | 0.0486343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.8627i | 1.18093i | 0.807063 | + | 0.590465i | \(0.201056\pi\) | ||||
−0.807063 | + | 0.590465i | \(0.798944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.4142 | − | 14.5139i | 0.627155 | − | 0.554547i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.1768i | 0.617183i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −33.6531 | −1.28208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.6991 | −1.05372 | −0.526862 | − | 0.849951i | \(-0.676631\pi\) | ||||
−0.526862 | + | 0.849951i | \(0.676631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.80606i | 0.106594i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.14903 | + | 3.56134i | 0.119450 | + | 0.135089i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 10.8510i | − | 0.411010i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.4690 | 0.698561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.9643 | −1.47166 | −0.735831 | − | 0.677166i | \(-0.763208\pi\) | ||||
−0.735831 | + | 0.677166i | \(0.763208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.37470i | − | 0.278142i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.38787 | − | 7.22425i | −0.240581 | − | 0.272081i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.1965i | 1.43653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.32250 | 0.162335 | 0.0811674 | − | 0.996700i | \(-0.474135\pi\) | ||||
0.0811674 | + | 0.996700i | \(0.474135\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.35026 | −0.0506388 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.84955i | 0.144167i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.57452 | − | 7.58181i | 0.320669 | − | 0.283544i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 19.3258i | − | 0.721736i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.3996 | −1.43206 | −0.716032 | − | 0.698067i | \(-0.754044\pi\) | ||||
−0.716032 | + | 0.698067i | \(0.754044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.7743 | 1.70473 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 28.5501i | − | 1.06179i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.46168 | + | 11.8496i | −0.0542855 | + | 0.440081i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.6728i | 0.803798i | 0.915684 | + | 0.401899i | \(0.131650\pi\) | ||||
−0.915684 | + | 0.401899i | \(0.868350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.7513 | −0.471624 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 25.0698i | − | 0.925976i | −0.886365 | − | 0.462988i | \(-0.846777\pi\) | ||
0.886365 | − | 0.462988i | \(-0.153223\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.46405 | − | 1.29455i | 0.0540023 | − | 0.0477503i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.7005i | − | 0.394159i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.9018 | −0.695312 | −0.347656 | − | 0.937622i | \(-0.613022\pi\) | ||||
−0.347656 | + | 0.937622i | \(0.613022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −23.4156 | −0.860195 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 43.6688i | 1.60205i | 0.598629 | + | 0.801026i | \(0.295712\pi\) | ||||
−0.598629 | + | 0.801026i | \(0.704288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.3127 | + | 13.9248i | 0.451101 | + | 0.510164i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.806063i | 0.0294923i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.4650 | 0.967010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 47.0541 | 1.71703 | 0.858514 | − | 0.512789i | \(-0.171388\pi\) | ||||
0.858514 | + | 0.512789i | \(0.171388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.1998i | 0.845448i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.6253 | − | 25.5877i | −0.823419 | − | 0.931231i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.9116i | − | 0.978119i | −0.872250 | − | 0.489059i | \(-0.837340\pi\) | ||
0.872250 | − | 0.489059i | \(-0.162660\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6859 | 0.604865 | 0.302432 | − | 0.953171i | \(-0.402201\pi\) | ||||
0.302432 | + | 0.953171i | \(0.402201\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 43.2163i | − | 1.56454i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.61213 | + | 6.73084i | −0.275217 | + | 0.243354i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 67.9511i | − | 2.45357i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.2995 | −0.840201 | −0.420100 | − | 0.907478i | \(-0.638005\pi\) | ||||
−0.420100 | + | 0.907478i | \(0.638005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.8872 | −0.392092 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.63656i | 0.0588631i | 0.999567 | + | 0.0294316i | \(0.00936971\pi\) | ||||
−0.999567 | + | 0.0294316i | \(0.990630\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.589104 | + | 4.77575i | −0.0211612 | + | 0.171550i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.52373i | − | 0.162288i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.9234 | 0.391370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.35026 | 0.263013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.38787i | 0.0853356i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.7480 | − | 10.3879i | 0.419304 | − | 0.370759i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.09095i | 0.0745344i | 0.999305 | + | 0.0372672i | \(0.0118653\pi\) | ||||
−0.999305 | + | 0.0372672i | \(0.988135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.11871 | 0.324635 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.5501 | 1.37068 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.5647i | 1.44049i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.73813 | − | 11.0132i | −0.345376 | − | 0.390597i | ||||
\(796\) | 0 | 0 |